Information on Result #714714
Linear OA(867, 98, F8, 36) (dual of [98, 31, 37]-code), using construction XX applied to C1 = C([8,36]), C2 = C([1,26]), C3 = C1 + C2 = C([8,26]), and C∩ = C1 ∩ C2 = C([1,36]) based on
- linear OA(842, 63, F8, 29) (dual of [63, 21, 30]-code), using the primitive BCH-code C(I) with length 63 = 82−1, defining interval I = {8,9,…,36}, and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(838, 63, F8, 26) (dual of [63, 25, 27]-code), using the primitive narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(848, 63, F8, 36) (dual of [63, 15, 37]-code), using the primitive narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(830, 63, F8, 19) (dual of [63, 33, 20]-code), using the primitive BCH-code C(I) with length 63 = 82−1, defining interval I = {8,9,…,26}, and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(812, 22, F8, 9) (dual of [22, 10, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(812, 23, F8, 9) (dual of [23, 11, 10]-code), using
- algebraic-geometric code AG(F,13P) [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using
- the Klein quartic over F8 [i]
- algebraic-geometric code AG(F,13P) [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using
- discarding factors / shortening the dual code based on linear OA(812, 23, F8, 9) (dual of [23, 11, 10]-code), using
- linear OA(87, 13, F8, 6) (dual of [13, 6, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(87, 14, F8, 6) (dual of [14, 7, 7]-code), using
- extended algebraic-geometric code AGe(F,7P) [i] based on function field F/F8 with g(F) = 1 and N(F) ≥ 14, using
- discarding factors / shortening the dual code based on linear OA(87, 14, F8, 6) (dual of [14, 7, 7]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(867, 49, F8, 2, 36) (dual of [(49, 2), 31, 37]-NRT-code) | [i] | OOA Folding | |